An Analysis of Non-Elliptic Curve Based Primality Tests

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Curve Based Primality Tests</title> <meta name="description" content="An Analysis of Non-Elliptic Curve Based Primality Tests"> <meta name="keywords" content="primality tests, Fermat鈥檚 primality test, Miller-Rabin primality test, Baillie-PSW primality test, AKS primality test"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img 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publication-listing mt-3 mb-3"> <h5 class="card-header" style="font-size:.9rem">An Analysis of Non-Elliptic Curve Based Primality Tests</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=William%20Wong">William Wong</a>, <a href="https://publications.waset.org/abstracts/search?q=Zakaria%20Alomari"> Zakaria Alomari</a>, <a href="https://publications.waset.org/abstracts/search?q=Hon%20Ching%20Lai"> Hon Ching Lai</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhida%20Li"> Zhida Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Modern-day information security depends on implementing Diffie-Hellman, which requires the generation of prime numbers. Because the number of primes is infinite, it is impractical to store prime numbers for use, and therefore, primality tests are indispensable in modern-day information security. A primality test is a test to determine whether a number is prime or composite. There are two types of primality tests, which are deterministic tests and probabilistic tests. Deterministic tests are adopting algorithms that provide a definite answer whether a given number is prime or composite. While in probabilistic tests, a probabilistic result would be provided, there is a degree of uncertainty. In this paper, we review three probabilistic tests: the Fermat Primality Test, the Miller-Rabin Test, and the Baillie-PSW Test, as well as one deterministic test, the Agrawal-Kayal-Saxena (AKS) Test. Furthermore, we do an analysis of these tests. All of the reviews discussed are not based on the Elliptic Curve. The analysis demonstrates that, in the majority of real-world scenarios, the Baillie- PSW test鈥檚 favorability stems from its typical operational complexity of O(log 3n) and its capacity to deliver accurate results for numbers below 2^64. <iframe src="https://publications.waset.org/abstracts/173827.pdf" style="width:100%; height:400px;" frameborder="0"></iframe> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=primality%20tests" title="primality tests">primality tests</a>, <a href="https://publications.waset.org/abstracts/search?q=Fermat%E2%80%99s%20primality%20test" title=" Fermat鈥檚 primality test"> Fermat鈥檚 primality test</a>, <a href="https://publications.waset.org/abstracts/search?q=Miller-Rabin%20primality%20test" title=" Miller-Rabin primality test"> Miller-Rabin primality test</a>, <a href="https://publications.waset.org/abstracts/search?q=Baillie-PSW%20primality%20test" title=" Baillie-PSW primality test"> Baillie-PSW primality test</a>, <a href="https://publications.waset.org/abstracts/search?q=AKS%20primality%20test" title=" AKS primality test"> AKS primality test</a> </p> <a href="https://publications.waset.org/abstracts/173827/an-analysis-of-non-elliptic-curve-based-primality-tests" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/173827.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">88</span> </span> </div> </div> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" 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An Analysis of Non-Elliptic Curve Based Primality Tests